A316883 - OEIS

%I #4 Jul 15 2018 14:13:32

%S 1,2,2,4,4,4,8,14,14,8,16,28,37,28,16,32,94,105,105,94,32,64,284,388,

%T 452,388,284,64,128,752,1280,2401,2401,1280,752,128,256,2244,4121,

%U 11532,18847,11532,4121,2244,256,512,6532,13933,54613,125218,125218,54613

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2.....4.......8.......16.........32..........64...........128

%C ...2....4....14......28.......94........284.........752..........2244

%C ...4...14....37.....105......388.......1280........4121.........13933

%C ...8...28...105.....452.....2401......11532.......54613........268142

%C ..16...94...388....2401....18847.....125218......843479.......6198339

%C ..32..284..1280...11532...125218....1187727....11791971.....128278641

%C ..64..752..4121...54613...843479...11791971...180224021....3018929955

%C .128.2244.13933..268142..6198339..128278641..3018929955...79732305036

%C .256.6532.46641.1322178.45184963.1404259002.51534776482.2144543383081

%H R. H. Hardin, <a href="/A316883/b316883.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

%F k=3: [order 15] for n>17

%F k=4: [order 61] for n>63

%e Some solutions for n=5 k=4

%e ..0..0..0..1. .0..1..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..1

%e ..0..0..0..1. .1..0..1..1. .0..0..0..1. .0..0..0..1. .0..1..0..1

%e ..0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..1. .0..1..1..1

%e ..1..1..1..0. .0..1..1..1. .0..0..0..1. .0..0..1..1. .0..0..1..1

%e ..1..1..1..1. .1..1..0..1. .1..1..0..0. .0..0..1..1. .0..1..0..1

%Y Column 1 is A000079(n-1).

%Y Column 2 is A304341.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 15 2018